Renormalisation-group study of crossover behaviour in an extended ϕ4 model on a square lattice

A real-space renormalisation group transformation is applied to study the order-disorder-displacive crossover in a phi 4 lattice model involving some nearest-neighbour and next-nearest-neighbour interactions. A non-trivial fixed point is found on the crossover surface. It is shown that the point is associated with a 'true' critical behaviour of the system. This critical behaviour is suggested to be a consequence of a continuous phase transition from a phase characterised by the appearance of locally ordered clusters and a long-range order between them to a more disordered high-temperature phase in which the clusters disappear.